“…To really have a complete image of the reasons why the temperature of the beverage plays such an important role during High Frequency fill level inspection, it results necessary to extend the notation for the dielectric permittivity ε out of the familiar field of Real numbers, to the field of Complex numbers…"

Thermal compensation            of the fill level inspection 


                   17 pages, 4.3 MB

Multivariate-related performances 

It is highly probable our Readers yet observed the occurrence of complete stops of the Filler Machine because of the excess of false rejects (false positives) by the Full Bottle Inspector controlling level and closure of their out feeding containers. If the Technology of that fill level control is High Frequency (short, HF) their most probable causes and solutions are described in the following.

The observed performances of the High Frequency fill level inspection (defects' detection ratio and false rejects' ratio) applied to a statistically significative population of containers, are heavily conditioned by the constancy of several factors.  

The main contributions, with a specific value for each one inspected container (they all random variables whose superposition is itself a random variable), accounting for nearly all of the performances' values established during containers' High Frequency fill level inspection, are:

  • ambient temperature, causing changes on the dielectric permittivity ε of the beverage, being this last in-the-ambient, then following ambient temperature tendencies;
  • ambient relative humidity of the air, causing biased results arising by a secondary contribution (air features its specific relative dielectric permittivity heavily different than that of water), added to the one of medium (the liquid in the container), whose Capacity of electrons is measured by the High Frequency fill level inspection bridge;
  • containers' speed, preventing a tilted upper surface of the liquid in the container;
  • physical properties of the beverage (e.g., density and kind of foaming, due to the Mixer and Carbonator Machines);
  • chemical properties of the beverage (e.g., molecular structure, foaming);
  • physical properties of the container (e.g., container height, diameter, shape, density, etc.);
  • chemical properties of the container (e.g., container molecular structure);
  • filler machine conditions (e.g., quality of the Filler Valve and of the filling setup during production);
  • foaming, affecting the beverage in the neck and head space area of the container.

Thermal ambient conditions and High Frequency fill level inspection

The macroscopic observation

We'll focus in the following only on the ambient thermal conditions.   It is widely known to the Production Staff of Bottling Lines, and particularly to those devoted to the area around the Filler Machine, that on restart after an extended stop of the Filler Machine, it has to be expected a diffucult phase.   The fill level control, immediately after the Filler Machine, shall be observed rejecting huge amounts of containers, filling in a few minutes the entire reject accumulation table, until stopping the Filler itself.   The reason is known.  Filler Machine stops, long enough to have implied a change on the thermal conditions of the Filler Machine heating it, shall imply the heating of the beverage in the Filler tank and related pipings.   This because a Filler Machine in stop conditions, starts to proceed toward a thermal equilibrium with the ambient, an equilibrium reached after an unavoidable hysteresis implicit in its huge metal mass and cold beverage contained in the tank.  High Frequency fill level inspection is particularly sensible to these occurrences, and transforms in a long and painful activity the restart operations of the Production Operators and their Shift Supervisors.

High Frequency fill level inspection, as detailed in other pages of this site, checks the beverage fill level in the neck of PET or glass bottles:

  • exposing the neck area to electromagnetic waves, whose frequency is ~ 21 MHz;
  • measuring the intensity of the electric alternate current crossing the impedance due to a "capacitor” where the bottle neck, its liquid or gaseous content and the interposed humid air, are the dielectric;
  • amplify, normalise in a definite range, digitise and compare this value with a pre-defined set range of acceptability;
  • finally, control an eventual request of rejection.

In the neck there is mainly water.  For a medium like water, base of the soft-drinks and beers of Beverage Bottling interest, there is a significant variation of the dielectric permittivity ε with temperature.   

The molecular level

Temperature is a measure of the average kinetic energy of the particles in a sample of matter, expressed in units of degrees on a standard scale. This is due to the effect of thermal energy on dipoles' orientational polarisation.  Because of this intimate molecular reason, the energetic level of the beverage whose level we want to inspect, really does matter.  Refer to the the following animation (credit University of Cambridge, Dept. of Materials Science and Metallurgy).    In the first, water dipoles are shown as vibrating system green-gray coloured and show a spreading of their polarisation angles directly related to the increase of temperature of the beverage.  

To have a complete image of the reasons why the temperature of the beverage  plays a role so important during fill level inspections, it results necessary to extend the notation for the dielectric permittivity ε out of the familiar field RC of Real numbers to the field of Complex numbers.   The Complex vector dielectric permittivity, for an em wave ω (wave number ω = 2 π ν ):                                      

                                        ε (ω)  =  ε′ (ω)  +  i ε′′ (ω)

has a real and an imaginary part, both representing components of the frequency response of the medium, differentiated following their phases:

                                                 ε′     in-phase          

                                                 ε′′    out-of-phase

and where:

                    ε′    →    refraction of the electromagnetic wave;

                    ε′′   →    absorption of the electronic, vibrational and rotational transitions;

This last imaginary component  i ε′′ (ω)  is  related  to  the  dissipation  of  energy  within  the medium.   Energy dissipation is related to the average molecular and bonds’ motion, say to the beverage water temperature.   Dielectric permittivity ε will change continously, as temperature decrease.   There are, however, several exceptions in the behaviour of the dielectric constant with respect to (beverage) temperature.   The fine-details of the process are out of our scopes and we'll only introduce the subject.   The dielectric constant ε will show discontinuities at phase boundaries, because the structure changes in a phase change.   Whether ε will increase or decrease at a given phase change, depends on the phases involved.   When an electric field is applied, like in the case of the High Frequency fill level inspections, the:

  • potential energy of orientations aligned with the electric field, is reduced;
  • energy of orientations aligned in opposition to the direction of the electric field, is increased.

For the particular case of beverages here considered, what precedes means that also during exposure to high frequency ( ν ~ 21 MHz ) electromagnetic waves ω:

  • less energy is required to exchange toward orientations aligned with the electric field;
  • more energy is required to pass to orientations aligned against the electric field.   

Therefore, with the passage of time, molecules of  water  will  become  aligned with the field.  What above synthesised by the following animation (credit University of Cambridge, Dept. of Materials Science and Metallurgy) referred to all mediums, water included.    The descending slope on right side of the "Tm" represents the liquid phase, the phase whose analysis we are  interested because of its relevance for Bottling applications.

Losses on production effects of an inspection choice

Choosing the High Frequency fill level inspection we are going to inspect that beverage level indirectly, measuring the intensity of the electric alternate current crossing the impedance due to a "capacitor” where the bottle neck, its liquid or gaseous content and the interposed humid air, are the dielectric.   Water temperature is directly influenced by the ambient temperature.    The Filler and pipings, around the beverage, represent the “ambient” as seen by the beverage point of view: a point of view we have to consider, being the beverage what we are controlling immediately later in the Inspector.  Being whatever Filler Machine based on a huge metal mass, it results faster than the water-based beverage to escalate toward the thermal equilibrium with the external ambient.   A Cooler (Heat-Exchanger), when present, reduces the dependence by external factors of the beverage temperature, before its reaches the Filler Machine, keeping in a set range the beverage temperature whatever the season, so that is the beverage in the end keeping constant the temperature of the Filler metallic mass.      But, is this truly observed along all of the year, in winter like in summer ?  Heat-exchangers are really and always accomplishing their desired task, keeping the beverage temperature in the desidered range, e.g.:  (4 - 8) C  at midnight like in the early afternoon ?       The area where the Filler Machine lies, always experiences sensible daily and seasonal differences of temperature, in the hours comprised between the coolest and hottest hours:

                                   coolest    ≈ 5 am   <   ≈  3  pm    hottest 

Direct examples in the figures down, representing temperatures measured in Hartsfield-Jackson Atlanta International Airport, Atlanta, USA, along 365 days from Oct. 20, 2012 until Oct 19, 2013.     A huge 37 C the seasonal range of temperatures.   37 C in a place not surely famous to experience extreme changes on ambient temperature during the entire year.  Diagrams (credit Vector Magic, Inc.) showing above the temperature and down the hourly temperatures.

Daily temperatures

Temperatures in Atlanta 2012 2013 and its relevance to evaluate the maximum range of temperatures expected for the beverage and the effect in terms of HF fill level inspection deviations

Above:  daily temperatures in Atlanta, USA, from October 20, 2012 til October 20, 2013.   The daily low (blue) and high (red) temperature with the area between them shaded gray and superimposed over the corresponding averages (thick lines), and with percentile bands (inner band from 25th to 75th percentile, outer band from 10th to 90th percentile).    The bar at the top of the graph is red where both the daily high and low are above average, blue where they are both below average, and white otherwise

Hourly temperatures

hourly temperature bands and their relevance to infer the maximum range of temperatures of the beverage and the effect in terms of HF fill level inspection deviations

Above:  the full year of hourly temperature reports with the days of the year on the horizontal and the hours of the day on the vertical. The hourly temperature measurement is color coded into meaningful temperature bands: frigid is purple (below -9°C), freezing is blue (-9°C to 0°C), cold is dark green (0°C to 10°C), cool is light green (10°C to 18°C), comfortable is yellow (18°C to 24°C), warm is light red (24°C to 29°C), hot is medium red (29°C to 38°C), sweltering is dark red (above 38°C), and missing data is pink

Considering what we saw in this Section about the:


          Above:  a Pt100  RTD  temperature sensor, particularly adapt for beverages 

  • relation between Beverage temperature and the effect on the measure of its fill level;
  • wide changes of the daily and seasonal temperatures around Bottling Lines;

it starts to be possible to fully understand why the High Frequency fill level inspection is so much intrinsically exposed to dagnine spontaneous variations of its own sensitivity. Spontaneous changes affecting the most delicate place of the entire Bottling Line: the Filler Machine out feed.  Yet with the less critical non-foaming beverages, leaving the HF fill level inspection sensitivity parameter constant along all of the year, they’ll be observed seasonal phases, where HF fill level inspection shall show opposite tendencies visible:

  • blocking completely the Bottling Line at the Filler out feed, because of false rejects during the cold season and hours;
  • not detecting (then, introducing to the Market), macroscopically underfilled containers, during the hottest season and hours.

To have a quantitative dimension of the problem, the same fill level inspection:

  • inspecting the same bottle format;
  • inspecting at the same height of the bridge;
  • running at the same speed;
  • at the same hour of the day;
  • in the out feed of the same Filler Machine in a non-thermostatic filling room;
  • in a Plant in the Boreal hemisphere;

shall provide on 10th of January a measurement ~ 20 % lower than on 10th of July.    What follows is obviously valid also for the Austral hemisphere, apart a de-phasing of 6 months.          A single annual setting for the HF under filling level inspection sensitivity,  one to be used along all of the following years is impossible at all; if set during:   

  • winter, say when the level in the neck is the minimum, it’d imply the missed rejection of grossly underfilled containers during summer season;
  • summer, say when the level in the mneck is maximum, it’d imply nearly 100 % of (false) rejects during winter season.

Visible effects of the changes on Beverage temperature: spontaneous changes of the HF fill level inspection sensitivity

What above allows to synthesise in two practical rules the temperature-related effects on false rejects:

  • increasing liquid temperature, forces the artificial reduction of both false rejection ratio (False Positives) and the detection ratio of the truly underfilled containers (True Positive);
  • decreasing liquid temperature, forces the artificial increase of both false rejection ratio (False Positives) and the detection ratio of the truly underfilled containers (True Positive).


Thermostatic-ambient solutions ?

It is possible, however practically unthinkable because anti-economic, to fully linearise the beverage temperature (a close alias of: 'beverage energy content') acting over the temperatures of all of the ambients and parts where those changes originates, say where the:

  • Filler Machine lies, e.g. keeping that ambient thermostatic;
  • pipings infeeding product to the Filler Machine;
  • Carbonator lies;
  • Buffer tank lies;
  • water and syrup pipings infeed the Carbonator (in case of soft-drinks or water);
  • pass the pipings joining Beer silos until Filler Machine beverage infeed (in case of beer).

Cooler-based solutions ?

More, a solution designed around a massive over sizing of the thermostatic Cooler, so to provide always and only beverage in an extremely strict range of temperatures, should also fail because:

  • of the expensive permanent power consumption;
  • Filler Machine and its related infeeding pipings, remain exposed to the changing thermal status of the ambient in which they all lie;
  • Filler Machine cannot assure constant production conditions at nominal speed.  It has its own periods of stop (or, slow speed motion), because being on CIP, Maintenance or (weekend) Stop.  During these non-Production phases, the ambient returns to unavoidably increase (or, decrease) the temperature of its metallic mass and of the related pipings.

A final and economic solution

Resistance versus Temperature

To counter the natural tendence of the beverage in the Filler tank to reach equilibrium with the ambient is possible, but not viable.   However, they really exist ways to pass around this source of problems.   Electronic Inspectors, as an optional, can be equipped with optional hardware-software modules consisting of a sensor of temperature installed into the filling tank.   These cheap systems:

  1. measures the beverage temperature directly into the filling tank with a common temperature sensor;
  2. Data are later processed by an Analog to Digital converter card, so to normalise analog values (equivalent to the measured temperature) into a fixed range;
  3. combine this data with the one obtained in the meantime, for the same container, by the High Frequency fill level measurement.  This way, it is possible a compensation for the however unavoidable seasonal superimposed to hourly variations for the ambient temperature of the ambient where they lie Filler Machine and related pipings.

Actually, these small optionals are not in the price-list of all of the Vendors of Electronic Inspectors of the world but, at least, in the price-list of the biggest.   The diagram on right side down, shows an example of relation between the Resistance of an RTD sensor and the corresponding measured Temperature.   RTD are passive measurement devices. They have to be supplied with an excitation current, then reading the voltage across their terminals.  The readout value finally converted  to temperature by mean of a simple algorithm.    Pt100 is the model commonly adopted, where 0 C is equivalent to 100 ohm.  Sensors are connected to dedicated circuits into the Electronic Inspector, providing: 

  • stable sources of power for the Temperature sensor; 
  • signal amplification;
  • analog-to-digital (AD) conversion.   

The out feed of the AD converter is a signal ready for a statistical-only, however yet very useful, attribution to containers entering the Shifting-Register of the most common Standalone-configured Electronic Inspectors.  An individual attribution to each one specific container requires an Electronic Inspector configured in-the-Machine, say with location sensors in the Filler and enough Triggers on Filler out feed Conveyor as to allow containers' tracking. 

On side, an example showing the linearity of a temperature to resistance correspondance, in               the wide range of temperatures:  (-300;  900) C

In the reality, the beverage into the Filler Machine amounts to several cubic meters (several tens of hectoliters): a mass like this of liquid cannot experience a sensible change on its temperature along only 2-10 seconds of time.  Then, the cheapest Standalone Bottling Control configuration yet reveals its full usefulness.   To containers' measurement of fill level results this way added a second property: the temperature (index of the energetic content) of the beverage for which that fill level has been measured.  Thanks to circuits like these, it becomes finally viable a permanent, and particularly sensible, setup of the reject threshold of the High Frequency fill level inspection.

Above:  temperature-equivalent analog signal measurement, amplification and AD digitalisation circuit.  In the image, a 4-wires sensor set to operate in 3-wire mode.  Beverage Temperature compensation is a must option for the Bottler interested in elimination of losses (false rejects and lost time of Production) and in the simultaneous increase of the product Quality Assurance with respect to containers' fill level.   A particularly sensitive setting of the reject threshold parameter of the HF fill level inspection, finally becomes viable

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